1. What is Critical Velocity in Gravitation?

Definition: Critical velocity (or escape velocity) is the minimum speed needed for an object to break free from a massive body's gravitational attraction without further propulsion.

Purpose: This calculation is essential in astrophysics, space exploration, and understanding celestial mechanics.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V_c \) — Critical velocity (m/s)
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²)
• \( M \) — Mass of the celestial body (kg)
• \( r \) — Distance from the center of mass (m)

Explanation: The formula calculates the velocity where an object's kinetic energy equals the gravitational potential energy.

3. Importance of Critical Velocity

Details: Understanding escape velocity is crucial for space mission planning, satellite launches, and studying planetary atmospheres.

4. Using the Calculator

Tips: Enter the mass of the celestial body, radius from its center, and gravitational constant (default provided). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's Earth's escape velocity?
A: Approximately 11.2 km/s (using Earth's mass 5.972 × 10²⁴ kg and radius 6.371 × 10⁶ m).

Q2: Does atmosphere affect escape velocity?
A: The formula gives theoretical value without atmospheric drag, which requires additional energy.

Q3: How does escape velocity vary with altitude?
A: It decreases with increasing distance from the center of mass (larger r in formula).

Q4: What if an object exceeds escape velocity?
A: It will leave the gravitational influence with residual velocity (hyperbolic trajectory).

Q5: Why is G so small in value?
A: Gravity is extremely weak compared to other fundamental forces, hence the tiny constant.